Washington — The President has apparently scored well with the American public through his new Mideast peace initiative.
First reaction from those who would be his severest critics, from the Jewish community, is one of relative approval. It appears to welcome Mr. Reagan's expressions of commitment to Israel's security and his rejection of an independent Palestinian state even while questioning the ''freeze'' he would impose on West Bank settlements.
Beyond disarming somewhat those who could potentially be his severest critics , the President - as reflected in congressional reaction and messages sent to the White House in response to his speech - has won the tentative approval of the public.
For some time now national polls have shown a growing impatience among Americans for what many see as a tendency for Israel, and, particularly, Prime Minister Menachem Begin, to go it alone - often disregarding US policy or wishes.
Now the President is perceived, it seems, as having come up with a Mideast plan that essentially says, as Mideast expert Joseph J. Sisco points out, ''If Israel can work out its independent course, we, too, can work out and present our independent course.''
Mr. Sisco, meeting with reporters over breakfast Sept. 2, said he had had an input into this Reagan peace plan and ''was briefed on it before it was presented.''
It also became clear to the millions who watched Reagan on television Wednesday night that he was fully involving himself in the search for peace in the Mideast.
''It's not a Jimmy Carter desk-officer negotiation,'' says Sisco. ''He now is making the key decisions.''
Meanwhile, former President Carter Thursday endorsed the new peace plan and rejected Israel's claim that it breached the Camp David accords he helped negotiate.
Sisco criticized Reagan for staying on the Mideast sidelines for 20 months. ''I've worked closely in this area with six presidents,'' said Sisco, ''and I've found that only with such personal presidential involvement can any real results be achieved.''
Presidential watchers here also make this assessment of the President:
* His leadership image has been measurably improved because he is seen now as standing up to Mr. Begin instead of apparently giving in, again and again.
However, this is not an anti-Israel public attitude. US polls show that pro-Israel sentiment still is more than 50 percent. A Gallup poll, completed before the evacuation of the Palestine Liberation Organization from Beirut, shows 56 percent of Americans give Israel a favorable rating while 36 oppose it. That is, however, a considerable drop from a 1981 poll that showed a 75 percent favorable rating, with 19 percent unfavorable.
During the presidential campaign, Reagan drew off a lot of Jewish votes - votes that Jimmy Carter, as a Democrat, would normally have received.
This attitude will persist, says Sisco ''because Reagan, in his speech, didn't imply that there should be a Palestinian homeland, as Carter did. Also, Reagan said there is to be no independent Palestinian state - and Carter never said that.''
* The President's image as a communicator has been further enhanced. Both reporters and congressmen are assessing his Mideast address as perhaps the best he has given thus far, both in the way it was written and in the way it was delivered.
* Finally, some observers say Reagan's participation in Mideast decisionmaking marks a turning point: that from now on he will be spending more time on foreign policy and less on the economy.